Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2412.13043

DiFfRG: A Discretisation Framework for functional Renormalisation Group flows

Franz R. Sattler·Jan M. Pawlowski
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce DiFfRG (Discretisation Framework for functional Renormalisation Group flows), a comprehensive computational C++ framework for solving functional Renormalisation Group flows in very general truncation schemes. Its central features are threefold: Firstly, the use of Finite Element Methods (FEM) for efficient, easy to set up and quantitatively reliable computations of field dependences. Secondly, the (simultaneous) setup of large, fully momentum-dependent vertex expansions. Thirdly, efficient time-discretisation methods, incorporating insights from studies of solving theories which exhibit spontaneous symmetry breaking, going hand in hand with shocks and an exponential increase of the information flow velocity in field space. The framework provides a Mathematica package for automatic code generation of flow equations, finite and zero temperature integration routines with support for GPU hardware and extensive parallelisation capabilities. Detailed examples and tutorials are provided and discussed herein which showcase and introduce the framework to the user. We illustrate the capabilities of DiFfRG with four examples, with the complete codes fully included: finite temperature O(N) theory, a Quark-Meson model, SU(3) Yang-Mills theory and four-Fermi flows in the QCD phase diagram.

Explore related subjects

hep-phcond-mat.stat-mechhep-thphysics.comp-phphysics.flu-dyn

Keep this discovery

BibTeXRIS

Franz R. Sattler, Jan M. Pawlowski. 2024-12-17. DiFfRG: A Discretisation Framework for functional Renormalisation Group flows. https://arxiv.org/abs/2412.13043

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Axionic Wormholes in Metric-Affine Gravity

The axion is a promising candidate for solving the strong CP problem. To solve this problem, the global U(1) symmetry must be preserved to a high degree of accuracy. However, it is well known that global symmetries are explicitly violated by quantum gravity effects, giving rise to what is referred to as the axion quality problem. In this paper, we investigate axionic wormholes as a source of explicit U(1) violation in Metric-Affine Gravity. This framework allows for spacetime torsion and non-metricity, which accommodate additional curvature-like and topological terms, such as the Holst and Nieh--Yan terms, that are absent from the metric and Palatini formalisms. We show that non-minimal couplings to these terms modify the wormhole dynamics and enhance the Euclidean wormhole action, thereby alleviating the axion quality problem. We also find that the viable parameter space is enlarged when two of these couplings are simultaneously present. We further identify representative parameter regions where the alleviation of the axion quality problem is compatible with inflationary constraints.

hep-ph↗
arXiv2026

Qubit-Qutrit Quantum Tomography of hadronic $\Lambda\phi$ and $\Lambda K^{\ast 0}$ systems

Quantum-information observables have emerged in recent years as new tools in nuclear and particle physics, from entanglement in top-quark pairs to spin correlations in $\Lambda\bar{\Lambda}$ production. Extending these studies to unequal-spin hadronic final states poses a fundamental challenge: the $6\times6$ density matrix of a qubit-qutrit system contains 35 independent spin parameters, but the decays of $\Lambda V$ pairs, with $V=\phi$ or $K^{*0}$, provide access to only 23 due to the hidden vector polarization from the strong decay. In this Letter, we formulate a qubit-qutrit quantum tomography (QQQT) technique for these spin-$\tfrac{1}{2}\otimes1$ systems and establish exact criteria for entanglement certification from the \textit{incomplete} density matrix. Compared with the $\Lambda\bar{\Lambda}$ system, QQQT of $\Lambda\phi$ and $\Lambda K^{*0}$ provides a new probe of nonperturbative QCD hadronization, enabling a direct comparison of the spin evolution of entangled quark pairs produced from the vacuum as they hadronize into a baryon or a vector meson.

hep-ph↗
arXiv2026

Twist decomposition of exclusive heavy meson production cross sections

We study the twist decomposition of the total cross sections for exclusive heavy vector meson electroproduction and photoproduction in the $\gamma^\ast p$ processes, within the leading logarithmic $1/x$ BFKL formalism. The Mellin transforms of the impact factors of the vector meson are calculated. We show that the higher twist contributions are strongly suppressed in the low-$x$ kinematical regime. Possible enhancement of the higher twists effects for nuclei targets is discussed.

hep-ph↗